Dependence of the Density of States on the Probability Distribution. Part II: Schrodinger Operators on R-d and Non-compactly Supported Probability Measures
We extend our results in Hislop and Marx (Int Math Res Not, 2018. https://doi.org/10.1093/imrn/rny156) on the quantitative continuity properties, with respect to the single-site probability measure, of the density of states measure and the integrated density of states for random Schrödinger operators. For lattice models on Z(d), with d >= 1, we treat the case of non-compactly supported probability measures with finite first moments. For random Schrödinger operators on R-d, with d >= 1, we prove results analogous to those in Hislop and Marx (2018) for compactly supported probability measures. The method of proof makes use of the Combes-Thomas estimate and the Helffer-Sjostrand formula.
Hislop, Peter D., and Christopher A. Marx. 2020. "Dependence of the Density of States on the Probability Distribution. Part II: Schrödinger Operators on R-d and Non-compactly Supported Probability Measures." Annales Henri Poincaré 21(2): 539-570.
Annales Henri Poinpcaré: A Journal of Theoretical and Mathematical Physics